Preheat the oven to 180°C/375°F fan. Line a 7.5 x 9.75-inch (19 x 25 cm) rectangular or 9-inch (23cm) square brownie pan with baking paper.
Break the chocolate up into chunks. Place into a medium pot with the butter and vegetable oil. Set over a low heat on the stove and stir often (to prevent it burning), until the chocolate is almost fully melted. Remove from the heat and set aside so the remaining chocolate can melt from the residual heat.
This next step can be done in a stand mixer with the whisk attachment, or in a large bowl with electric beaters: Place the eggs, egg white, salt and both kinds of sugar into a large bowl (or the bowl of the stand mixer) and whisk until pale and very fluffy. Add the water and vanilla then continue to whisk until the sugar has mostly dissolved - you can tell when this has happened by rubbing some of the mixture between your fingertips, if it feels very grainy, you need to keep whisking. This will take about 10-15 minutes.
Mix the cocoa powder and sourdough starter into the melted chocolate mixture until completely combined.
Add this mixture to the bowl of whipped egg mixture and fold together until just combined.
Pour into the prepared brownie tin and bake for 30-35 minutes (SEE NOTES). The top should look dry and a toothpick inserted into the centre of the brownies should come out with a little bit of batter still stuck to it, but not LOADS.
Let the brownies cool for at least 20 minutes before slicing into 16. Sprinkle with some flaky salt if you want!